量子变分激活函数赋能Kolmogorov-Arnold网络
Quantum Variational Activation Functions Empower Kolmogorov-Arnold Networks
September 17, 2025
作者: Jiun-Cheng Jiang, Morris Yu-Chao Huang, Tianlong Chen, Hsi-Sheng Goan
cs.AI
摘要
变分量子电路（VQCs）是量子机器学习中的核心，而近期在Kolmogorov-Arnold网络（KANs）上的进展凸显了可学习激活函数的强大能力。我们通过引入量子变分激活函数（QVAFs）统一了这两个方向，这些函数通过称为数据重上传激活网络（DARUANs）的单量子比特数据重上传电路实现。我们展示了在数据预处理中具有可训练权重的DARUAN随着数据重复次数增加，其频率谱呈指数增长，从而在不损失表达能力的前提下，相比基于傅里叶的激活函数实现了参数规模的指数级缩减。将DARUAN嵌入KANs中，形成了量子启发的KANs（QKANs），它们在保持KANs可解释性的同时，提升了参数效率、表达能力和泛化性能。我们进一步引入了两种新技术以增强可扩展性、可行性和计算效率，例如层扩展和作为多层感知机（MLPs）即插即用替代的混合QKANs（HQKANs），适用于大规模模型中的前馈网络。我们提供了理论分析，并在函数回归、图像分类和自回归生成语言建模上进行了广泛实验，证明了QKANs的效率和可扩展性。DARUANs和QKANs为在噪声中等规模量子（NISQ）硬件和经典量子模拟器上推进量子机器学习提供了一个有前景的方向。
English
Variational quantum circuits (VQCs) are central to quantum machine learning,
while recent progress in Kolmogorov-Arnold networks (KANs) highlights the power
of learnable activation functions. We unify these directions by introducing
quantum variational activation functions (QVAFs), realized through single-qubit
data re-uploading circuits called DatA Re-Uploading ActivatioNs (DARUANs). We
show that DARUAN with trainable weights in data pre-processing possesses an
exponentially growing frequency spectrum with data repetitions, enabling an
exponential reduction in parameter size compared with Fourier-based activations
without loss of expressivity. Embedding DARUAN into KANs yields
quantum-inspired KANs (QKANs), which retain the interpretability of KANs while
improving their parameter efficiency, expressivity, and generalization. We
further introduce two novel techniques to enhance scalability, feasibility and
computational efficiency, such as layer extension and hybrid QKANs (HQKANs) as
drop-in replacements of multi-layer perceptrons (MLPs) for feed-forward
networks in large-scale models. We provide theoretical analysis and extensive
experiments on function regression, image classification, and autoregressive
generative language modeling, demonstrating the efficiency and scalability of
QKANs. DARUANs and QKANs offer a promising direction for advancing quantum
machine learning on both noisy intermediate-scale quantum (NISQ) hardware and
classical quantum simulators.